Computing the Diameter of 17-Pancake Graph Using a PC Cluster

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An n-pancake graph is a graph whose vertices are the permutations of n symbols and each pair of vertices are connected with an edge if and only if the corresponding permutations can be transitive by a prefix reversal. Since the n-pancake graph has n! vertices, it is known to be a hard problem to compute its diameter by using an algorithm with the polynomial order of the number of vertices. Fundamental approaches of the diameter computation have been proposed. However, the computation of the diameter of 15-pancake graph has been the limit in practice. In order to compute the diameters of the larger pancake graphs, it is indispensable to establish a sustainable parallel system with enough scalability. Therefore, in this study, we have proposed an improved algorithm to compute the diameter and have developed a sustainable parallel system with the Condor/MW framework, and computed the diameters of 16- and 17-pancake graphs by using PC clusters.